>The DAML-OIL suggestions defines Thing as the union of Nothing and the
>complement of Nothing and stated - but does not explains why - that this
>provide some benefits regarding semantics?
>
>My current perspective is from outside DAML and DL so I hope that the
>following make sense and is not too misaligned with the proposal::
>
>I would like to see the ability to (on a individual basis) express which
>nodes/classes/instances/etc are in the (current) universe (domain) of
>discourse and which are not.
>
>For this one approach is to be able to specify what is "outside", for
>which it appears that it would be a good idea to define Nothing simply
>as the complement of Thing with the usual IC(Thing) = DD.... Than
>individuals of Nothing would be outside the universe of discourse.
In general it is always possible to take a lattice-like heirarchy
with a top and bottom element and 'wrap' it inside a larger similar
structure by adding a higher top and a lower bottom. The issue here
is whether we want to be able to give a name to what are seen as the
global extremes, so that any subsequent additions must 'fit inside'
these, or whether any such structure is seen as extendable to a
larger one. Either strategy is workable, but I think the latter is
the most useful.
I would urge that Morten's suggestion be adopted, if I follow him
correctly. The idea then would be that every DAML ontology is
understood to be 'about' a universe of discourse, and that Nothing
and Thing are understood as relative to that universe. This allows
one ontology to align its universe with another by asserting that its
Thing and Nothing are equivalent to the other ontology's , but it
also allows an ontology to claim a larger universe of discourse by
asserting that B#Thing is equivalent to some class name in its
heirarchy (and B#Nothing to its complement) thus restricting all the
relations imported from the ontology B to the appropriate class in
its heirarchy. If this is workable, the complementarity of Thing and
Nothing can be preserved in each ontology, even though the exact
meanings are implicitly indexed by the ontology they occur in.
Pat Hayes
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